Sparse Dictionary-based Attributes for Action Recognition and Summarization

We present an approach for dictionary learning of action attributes via information maximization. We unify the class distribution and appearance information into an objective function for learning a sparse dictionary of action attributes. The objective function maximizes the mutual information between what has been learned and what remains to be learned in terms of appearance information and class distribution for each dictionary atom. We propose a Gaussian Process (GP) model for sparse representation to optimize the dictionary objective function. The sparse coding property allows a kernel with compact support in GP to realize a very efficient dictionary learning process. Hence we can describe an action video by a set of compact and discriminative action attributes. More importantly, we can recognize modeled action categories in a sparse feature space, which can be generalized to unseen and unmodeled action categories. Experimental results demonstrate the effectiveness of our approach in action recognition and summarization

Reconstruction of Frequency Hopping Signals From Multi-Coset Samples

Multi-Coset (MC) sampling is a well established, practically feasible scheme for sampling multiband analog signals below the Nyquist rate. MC sampling has gained renewed interest in the Compressive Sensing (CS) community, due partly to the fact that in the frequency domain, MC sampling bears a strong resemblance to other sub-Nyquist CS acquisition protocols. In this paper, we consider MC sampling of analog frequency hopping signals, which can be viewed as multiband signals with changing band positions. This nonstationarity motivates our consideration of a segment-based reconstruction framework, in which the sample stream is broken into short segments for reconstruction. In contrast, previous works focusing on the reconstruction of multiband signals have used a segment-less reconstruction framework such as the modified MUSIC algorithm. We outline the challenges associated with segment-based recovery of frequency hopping signals from MC samples, and we explain how these challenges can be addressed using conventional CS recovery techniques. We also demonstrate the utility of the Discrete Prolate Spheroidal Sequences (DPSS's) as an efficient dictionary for reducing the computational complexity of segment-based reconstruction

Compressive sensing: a paradigm shift in signal processing

We survey a new paradigm in signal processing known as "compressive sensing". Contrary to old practices of data acquisition and reconstruction based on the Shannon-Nyquist sampling principle, the new theory shows that it is possible to reconstruct images or signals of scientific interest accurately and even exactly from a number of samples which is far smaller than the desired resolution of the image/signal, e.g., the number of pixels in the image. This new technique draws from results in several fields of mathematics, including algebra, optimization, probability theory, and harmonic analysis. We will discuss some of the key mathematical ideas behind compressive sensing, as well as its implications to other fields: numerical analysis, information theory, theoretical computer science, and engineering.Comment: A short survey of compressive sensin

Sparse and silent coding in neural circuits

Sparse coding algorithms are about finding a linear basis in which signals can be represented by a small number of active (non-zero) coefficients. Such coding has many applications in science and engineering and is believed to play an important role in neural information processing. However, due to the computational complexity of the task, only approximate solutions provide the required efficiency (in terms of time). As new results show, under particular conditions there exist efficient solutions by minimizing the magnitude of the coefficients (`$l_1$-norm') instead of minimizing the size of the active subset of features (`$l_0$-norm'). Straightforward neural implementation of these solutions is not likely, as they require \emph{a priori} knowledge of the number of active features. Furthermore, these methods utilize iterative re-evaluation of the reconstruction error, which in turn implies that final sparse forms (featuring `population sparseness') can only be reached through the formation of a series of non-sparse representations, which is in contrast with the overall sparse functioning of the neural systems (`lifetime sparseness'). In this article we present a novel algorithm which integrates our previous `$l_0$-norm' model on spike based probabilistic optimization for sparse coding with ideas coming from novel `$l_1$-norm' solutions. The resulting algorithm allows neurally plausible implementation and does not require an exactly defined sparseness level thus it is suitable for representing natural stimuli with a varying number of features. We also demonstrate that the combined method significantly extends the domain where optimal solutions can be found by `$l_1$-norm' based algorithms.Comment: 19 pages, 2 figures and 4 tables with pseudocode

Multilevel Illumination Coding for Fourier Transform Interferometry in Fluorescence Spectroscopy

Fourier Transform Interferometry (FTI) is an interferometric procedure for acquiring HyperSpectral (HS) data. Recently, it has been observed that the light source highlighting a (biologic) sample can be coded before the FTI acquisition in a procedure called Coded Illumination-FTI (CI-FTI). This turns HS data reconstruction into a Compressive Sensing (CS) problem regularized by the sparsity of the HS data. CI-FTI combines the high spectral resolution of FTI with the advantages of reduced-light-exposure imaging in biology. In this paper, we leverage multilevel sampling scheme recently developed in CS theory to adapt the coding strategy of CI-FTI to the spectral sparsity structure of HS data in Fluorescence Spectroscopy (FS). This structure is actually extracted from the spectral signatures of actual fluorescent dyes used in FS. Accordingly, the optimum illumination coding as well as the theoretical recovery guarantee are derived. We conduct numerous numerical experiments on synthetic and experimental data that show the faithfulness of the proposed theory to experimental observations.Comment: 5 pages, 4 figure

Compressive hyperspectral imaging via adaptive sampling and dictionary learning

In this paper, we propose a new sampling strategy for hyperspectral signals that is based on dictionary learning and singular value decomposition (SVD). Specifically, we first learn a sparsifying dictionary from training spectral data using dictionary learning. We then perform an SVD on the dictionary and use the first few left singular vectors as the rows of the measurement matrix to obtain the compressive measurements for reconstruction. The proposed method provides significant improvement over the conventional compressive sensing approaches. The reconstruction performance is further improved by reconditioning the sensing matrix using matrix balancing. We also demonstrate that the combination of dictionary learning and SVD is robust by applying them to different datasets

On the Conditioning of the Spherical Harmonic Matrix for Spatial Audio Applications

In this paper, we attempt to study the conditioning of the Spherical Harmonic Matrix (SHM), which is widely used in the discrete, limited order orthogonal representation of sound fields. SHM's has been widely used in the audio applications like spatial sound reproduction using loudspeakers, orthogonal representation of Head Related Transfer Functions (HRTFs) etc. The conditioning behaviour of the SHM depends on the sampling positions chosen in the 3D space. Identification of the optimal sampling points in the continuous 3D space that results in a well-conditioned SHM for any number of sampling points is a highly challenging task. In this work, an attempt has been made to solve a discrete version of the above problem using optimization based techniques. The discrete problem is, to identify the optimal sampling points from a discrete set of densely sampled positions of the 3D space, that minimizes the condition number of SHM. This method has been subsequently utilized for identifying the geometry of loudspeakers in the spatial sound reproduction, and in the selection of spatial sampling configurations for HRTF measurement. The application specific requirements have been formulated as additional constraints of the optimization problem. Recently developed mixed-integer optimization solvers have been used in solving the formulated problem. The performance of the obtained sampling position in each application is compared with the existing configurations. Objective measures like condition number, D-measure, and spectral distortion are used to study the performance of the sampling configurations resulting from the proposed and the existing methods. It is observed that the proposed solution is able to find the sampling points that results in a better conditioned SHM and also maintains all the application specific requirements.Comment: 12 pages; This paper is a preprint of a paper submitted to IET Signal Processing Journal. If accepted, the copy of record will be available at the IET Digital Librar

Dictionary learning under global sparsity constraint

A new method is proposed in this paper to learn overcomplete dictionary from training data samples. Differing from the current methods that enforce similar sparsity constraint on each of the input samples, the proposed method attempts to impose global sparsity constraint on the entire data set. This enables the proposed method to fittingly assign the atoms of the dictionary to represent various samples and optimally adapt to the complicated structures underlying the entire data set. By virtue of the sparse coding and sparse PCA techniques, a simple algorithm is designed for the implementation of the method. The efficiency and the convergence of the proposed algorithm are also theoretically analyzed. Based on the experimental results implemented on a series of signal and image data sets, it is apparent that our method performs better than the current dictionary learning methods in original dictionary recovering, input data reconstructing, and salient data structure revealing.Comment: 27 pages, 9 figures, 1 tabl

A Unified Approach to Sparse Signal Processing

A unified view of sparse signal processing is presented in tutorial form by bringing together various fields. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described succinctly. The common benefits of significant reduction in sampling rate and processing manipulations are revealed. The key applications of sparse signal processing are sampling, coding, spectral estimation, array processing, component analysis, and multipath channel estimation. In terms of reconstruction algorithms, linkages are made with random sampling, compressed sensing and rate of innovation. The redundancy introduced by channel coding in finite/real Galois fields is then related to sampling with similar reconstruction algorithms. The methods of Prony, Pisarenko, and MUSIC are next discussed for sparse frequency domain representations. Specifically, the relations of the approach of Prony to an annihilating filter and Error Locator Polynomials in coding are emphasized; the Pisarenko and MUSIC methods are further improvements of the Prony method. Such spectral estimation methods is then related to multi-source location and DOA estimation in array processing. The notions of sparse array beamforming and sparse sensor networks are also introduced. Sparsity in unobservable source signals is also shown to facilitate source separation in SCA; the algorithms developed in this area are also widely used in compressed sensing. Finally, the multipath channel estimation problem is shown to have a sparse formulation; algorithms similar to sampling and coding are used to estimate OFDM channels.Comment: 43 pages, 40 figures, 15 table

A Bayesian Nonparametric Approach to Image Super-resolution

Super-resolution methods form high-resolution images from low-resolution images. In this paper, we develop a new Bayesian nonparametric model for super-resolution. Our method uses a beta-Bernoulli process to learn a set of recurring visual patterns, called dictionary elements, from the data. Because it is nonparametric, the number of elements found is also determined from the data. We test the results on both benchmark and natural images, comparing with several other models from the research literature. We perform large-scale human evaluation experiments to assess the visual quality of the results. In a first implementation, we use Gibbs sampling to approximate the posterior. However, this algorithm is not feasible for large-scale data. To circumvent this, we then develop an online variational Bayes (VB) algorithm. This algorithm finds high quality dictionaries in a fraction of the time needed by the Gibbs sampler.Comment: 30 pages, 11 figure